On Cliques and Clique Chromatic Numbers in Line, Lict and Lictact Graphs

Abstract

The line graph of a graph G denoted as L(G) has vertex set E(G) in which two vertices are adjacent if they correspond to adjacent edges in G. The lict graph and litact graph of G, denoted as $L_c(G)$ and $L_{ct}(G)$, respectively having vertex set $E(G)\cup C(G)$ (here C(G) is the set of cut-vertices of G), two of these vertices will be adjacent in $L_c(G)$ if they correspond to adjacent edges of G or one vertex is an edge e of G and other vertex is a cut-vertex c of G such that e is incident to c; and two vertices in $L_{ct}(G)$ be adjacent if they are adjacent or incident elements of G. In this paper, we establish results on cliques and clique chromatic numbers in line, lict and litact graphs of any graph.